"Question 60
Find the probabilities below using a standard 52 card deck.

The graph that could be used to find the distance between the points

(-3, -13) and (11, 9) is given as follows:

B. graph of a right triangle with hypotenuse beginning at negative 3 comma negative 13 and ending at 11 comma 9.

What is distance between two points?

The distance between two points in a plane is the length of the line segment separating the two points. Typically, the equation

d=√((x2 - x1)^2 + (y2 - y1)^2) is used to calculate the distance between two points.

Suppose we have a pair of points, with the coordinates given as follows:

[tex](x_1, y_1)[/tex]  and  [tex](x_2, y_2)[/tex].

The two points form a right triangle, in which the sides are given as follows:

[tex]y_2-y_1\\x_2-x_1[/tex]

The distance between these two points is given by the hypotenuse of the right triangle.

Hence, applying the Pythagorean Theorem, the distance is obtained as follows:

[tex]d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}[/tex]

In this problem, the coordinates of the points are given as follows:

(−3, −13) and (11, 9).

Hence the correct option is given by option B.

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The age of the bones when they were discovered is 13439.66 years

What is half-life of an element?

The half-life of a radioactive isotope is the amount of time it takes for one-half of the radioactive isotope to decay. The half-life of a specific radioactive isotope is constant; it is unaffected by conditions and is independent of the initial amount of that isotope.

Half-life (symbol t½) is the time required for a quantity (of substance) to reduce to half of its initial value

The decay constant λ is = 0.693/t½

where t½ is the half-life of the element

Given data ,

The radioactive element​ carbon-14 has a​ half-life of 5750 years

So , the value of t½ = 5750 years

Now , the decay constant λ = 0.693 / t½

Substituting the values in the equation , we get

Decay constant λ = 0.693 / t½

Decay constant λ = 0.693 / 5750

Decay constant λ = 1.205 x 10⁻⁴

N=N₀e ^ −λt

where N₀ = Mass of radioactive element initially

N = Mass of radioactive element after time t

Apply natural logarithm on both the sides of the equation , we get

ln N = ln N₀ - λt

Let N0 be 100 then N will be 100 - 80.2 = 19.8

Substituting the values in the equation , we get

ln 19.8 = ln 100 -  1.205 x 10⁻⁴ ( t )

ln [ 19.8 / 100 ] = - 1.205 x 10⁻⁴ ( t )

-1.61948 = -1.205 x 10⁻⁴ ( t )

Therefore , the value of t is

t = -1.61948 / -1.205 x 10⁻⁴

t = 1.343966 x 10⁴

t = 13439.66 years

Therefore , the value of t is 13439.66 years

Hence ,

The age of the bones when they were discovered is 13439.66 years

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The following statements are true based on the frequency table:

Twice as many students prefer green than purple

And

Two more students prefer blue than purple

What is frequency table ?

The information that is gathered is called data. The quantity of occurrences of an event or value is referred to as its frequency. A frequency table is a table that lists items and displays how frequently each item happens.

From the frequency table,

Red= 6

yellow = 2

Blue = 5

Purple = 3

Green = 6

We can see that "Twice as many students prefer green than purple"

And

Two more students prefer blue than purple

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Answer:1400

Step-by-step explanation:

Answer:

the answer is 5

Step-by-step explanation:

(Add 10r to both sides)

-7-7r+10r= 8

Then -7+3r = 8

(Add 7 to both sides)

3r = 8+7

3r = 15

Divide both sides by 3.

r = 5

Answer:

Below

Step-by-step explanation:

y = - x^2 + 5       solve for x

y-5 = - x^2

x^2 = 5-y

x = ± sqrt (5-y)        now switch the x's and y's

y = ± sqrt(5-x)    

Here is a picture:

a) The hypotheses for this study would be the Null hypothesis and Alternative hypothesis.

b) The completed ANOVA summary table would be the Sum of Squares.

c) The calculator would give a p-value of approximately 0.03.

d) The results of the ANOVA test may not be reliable.

(a) The hypotheses for this study would be:

Null hypothesis ([tex]H_0[/tex]): There is no difference in the average lifetime of the four types of batteries.

Alternative hypothesis ([tex]H_1[/tex]): There is a difference in the average lifetime of the four types of batteries.

(b) The completed ANOVA summary table would be:

Sum of Squares (SS) df Mean Squares (MS) F

Between (Factor) 25.7375 3 8.578 3.77

Within (Error) 75 56 1.34

Total 100 59

(c) To find the p-value, you would use the Fcdf function on your calculator. The syntax for this would be Fcdf(F, 10000, df Between, df Within). In this case, the F value is 3.77, the df Between is 3, and the df Within is 56. Plugging these values into the calculator would give a p-value of approximately 0.03.

(d) Based on the p-value, we can reject the null hypothesis and conclude that there is a significant difference in the average lifetime of the four types of batteries. This suggests that the type of battery has an effect on its lifetime. However, it is important to note that this conclusion is based on the assumptions of the ANOVA test, including the assumption of equal variances among the groups. If these assumptions are not met, the results of the ANOVA test may not be reliable.

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The required average rate of change in the amount of Kendall's account is $50 per month.

Rate is a measurement to determine the change in one quantity with respect to another quantity.

Given that,

The amount of the end of the 8th month in Kendall's account = $450,

And at the end of the 11th month, the saved amount = $600.

To find the rate of change in saving amount

The increased amount = 600 - 450 = 150.

Since, In 3 months the amount increased by 150.

So, the average rate of change in amount

= 150 / 3.

= 50.

The average rate of change in the amount is $50 per month.

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The exponential function passes through the points (-1,4/5) and (1,20) will be y = 4 × [tex]5^{x}[/tex].

In mathematics, an exponential function is a relationship of the type y = ax, where x is an independent variable that spans the entire real number line and is expressed as the exponent of a positive number.

In other meaning, an exponential function is that function above which a variable x has imposed.

Suppose the exponential function as

y = a[tex]e^{bx}[/tex]

Substitute, (-1,4/5)

4/5 = a[tex]e^{-b}[/tex]                             (1)

Substitute, (1,20)

20 = a[tex]e^{b}[/tex]                                (2)

Multiply (1) with (2)

(4/5)20 = a[tex]e^{-b}[/tex] × a[tex]e^{b}[/tex]

4 × 4 = a²

a = 4

Substitute, a = 4 into (2)

20 = 4[tex]e^{b}[/tex]    

[tex]e^{b}[/tex] = 5

Take log on both sides of the above equation,

ln [tex]e^{b}[/tex]  =  ln 5

b = ln 5

Substitute a = 4 and b = ln 5 into y = a[tex]e^{bx}[/tex]

y = 4 e^(x(ln 5)) = 4 e^(ln5^x)

y = 4 × [tex]5^{x}[/tex]

Hence "The exponential function passes through the points (-1,4/5) and (1,20) will be y = 4 × [tex]5^{x}[/tex]".

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Answer:

x = -3

Step-by-step explanation:

If you look at the graph.

x = 4 is a vertical line.  

Another vertical line that would be parallel to this can contain the point (-3, 7) would be the line x = -3

The relationship between the cone cylinder and sphere is sphere takes up two-thirds of the volume of the cylinder, the cone takes up one-third of the volume of the cylinder.

Answers of blank :

Blank 1 = 1/3

Blank 2 = Three

Blank 3 = Two

Blank 4 = 2/3

Blank 5 = 1/3

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Answer:

#4 x=70

Step-by-step explanation:

Because this is an Isosceles triangle, we know that the 2 base angles have to be equivalent. So subtract 40 from 180 which leaves you with 140, then divide 140 by 2 because there are 2 base angles. Then arrive at the answer of x=70.

-Hope this helped & Happy Holidays!

In linear equation, Samuel bought 7 bags of popcorn and 10 bags of candies.

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

                              Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Let x represent the number of bags of popcorn and y represent the number of candies that Samuel bought.

She bought $43.75 worth of bags of popcorn and candies. Hence:

5x + 4.75y = 43.75  ...........  (1)

She bought a total of 17 bags of popcorn and candies altogether. Hence:

x + y = 9       (2)

Solving equations 1 and 2 simultaneously gives:

x = 4, y = 5

Therefore Samuel bought 4 bags of popcorn and 5 bags of candies.

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The constant of proportionality will be 9.5 when the table displays the proportionate cost for a particular quantity of golf ball buckets at a driving range.

Given that,

The table displays the proportionate cost for a particular quantity of golf ball buckets at a driving range.

We have to find the constant of proportionality.

We know that,

A collection of consecutively ordered numbers a and b expressed as a/b, where b is never equal to zero, is referred to as a ratio. A statement is considered proportionate when there is equality between two items.

The table displays the proportional relationship between the price for a particular quantity of golf ball cans at a driving range.

Buckets                         3               5             7

Price (dollars)            28.50       47.50      66.50

The constant of proportionality is calculated as,

⇒ 25.8 / 3

⇒ 9.5

Therefore, The constant of proportionality will be 9.5 when the table displays the proportionate cost for a particular quantity of golf ball buckets at a driving range.

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Answer:

9.5

Step-by-step explanation:

I took the exam and got it right

The distribution is bimodal. -  this is a correct statement.

According to the question, the following distribution is 5, 5, 8, 9, 10, 10, and 11.

        In the above distribution, there are two modes i,e 5 and 10.

                 Median:  Middle value

                In the above distribution, the median is - 9.

        Mean =  [tex]\frac{5 + 5 + 8 + 9 + 10 + 10 + 11}{7}[/tex]  = [tex]\frac{58}{7}[/tex] = 8.28

Hence,

The distribution is bimodal. -  this is a correct statement.

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Answer: D

Step-by-step explanation:

B = -6.3

F = -5

M = -4.5

A.) -6.3 is not greater than -4.5

B.) -5 is not less than -6.3

C.) -4.5 is not less than -5

D.) -5 is less than -4.5

Each person got 16 fish equally divided among 7 fishermen.

A mathematical statement expressed as a string of numbers and unknowable variables is known as a numerical expression. Statements can be used to create numerical expressions.

Given, One fisherman and 6 his friends were fishing.

So, The total no. of people is (6 + 1) = 7.

one decided to go home so he took 48 fish which was 3/7 of all fish in the box.  

Let, 'x' be the total no. of fish.

Therefore, (3/7)x = 48.

x = 48×(7/3).

x = 112.

Now, by dividing the total no. of fish by total no. of fishermen

we get, (112/7).

= 16.

So, Each person got 16 fish.

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The slope of the line perpendicular to 4x - 6y = - 60 is (-3/2).

The slope is the rate of change of the y-axis with respect to the x-axis.

The equation of a line in slope-intercept form is

y = mx + b, where

slope = m and y-intercept = b.

We know the greater the absolute value of a slope is the more steeper is it's graph or rate of change is large.

We know lines perpendicular to each other have slopes that are negative reciprocals of each other.

Given line is 4x - 6y = - 60 ⇒ - 6y = - 4x - 60 ⇒ y = (2/3)x + 10.

Now the line perpendicular to it will have a slope of (-3/2).

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340 ft high

d = 400' distance from building to tower

26° from the window to the top of the tower and 20° from the window to the bottom of the tower

Tan 26 = h2/d  

Tan 20 = h1/d  

h2 = 400Tan26

h1 = 400Tan20

on solving the equations,

h=a+b

Tower = 340 ft high

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well, since we know there are 180° in π/2 radians, then, what's 5π/7 radians?

[tex]\begin{array}{ccll} degrees&radians\\ \cline{1-2} 180&\frac{\pi }{2}\\[1em] d&\frac{5\pi }{7} \end{array}\implies \cfrac{180}{d}~~ = ~~\cfrac{\frac{\pi }{2}}{ ~~ \frac{5\pi }{7} ~~ }\implies \cfrac{180}{d}=\cfrac{\pi }{2}\cdot \cfrac{7}{5\pi } \\\\\\ \cfrac{180}{d}=\cfrac{7}{10}\implies 1800=7d\implies \cfrac{1800}{7}=d\implies 257.14^o\approx d[/tex]

The required percent of the coffee left is given as 66.67%.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
24 ounces of coffee Ms. Bobadilla,
And 8 ounces of coffee has been drinking,
Applying the percentage evaluation, in order to calculate the remaining coffee to Ms. Bobadilla.
Percentage of coffee remaining = 24 - 8 / 24 × 100%
Percentage of coffee remaining = 0.6667 × 100%
Percentage of coffee remaining = 66.67%

Thus, the percentage is given as 66.67%.

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A confidence interval that will capture the true population mean with 95% confidence. The value is ( 23.6459    , 24.8293 ) .

What is population mean?

A population in statistics is a group of comparable objects or occurrences that are relevant to a particular topic or experiment. A statistical population can be a collection of real things or a hypothetical, possibly limitless collection of objects derived from experience.

Data: 18

for given data

[tex]$$\begin{aligned}\bar{X} & =\frac{\sum X i}{n} \\& =2448 / 101 \\& =24.2376\end{aligned}$$[/tex]

as population variance is unknown so we used sample variance

[tex]$$\begin{aligned}S^2 & =\frac{1}{n-1}\left(\sum X i^2-n \times \bar{X}^2\right) \\S^2 & =\frac{1}{100}\left(60232-101 \times 24.2376^2\right) \\& =8.9830\end{aligned}$$[/tex]

Now

[tex]\frac{\bar{X}-\mu}{S / \sqrt{n}} \sim t_{n-1}$$[/tex]

hence 95 % of population mean is

As n=101 which is large so critical value is 1.98397

[tex]$$\begin{aligned}& =\left(\bar{X}-\sqrt{\frac{S}{n}} \times t_{(n-1, \alpha / 2)}, \bar{X}+\sqrt{\frac{S}{n}} \times t_{(n-1, \alpha / 2)}\right) \\& =\left(24.2376-\sqrt{\frac{8.9830}{101}} \times 1.98397,24.2376+\sqrt{\frac{8.9830}{101}} \times 1.98397\right) \\& =(23.6459,24.8293)\end{aligned}$$[/tex]

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Answer:

------------------------------

Equation of line:

Given values can be interpreted as pairs of coordinates of the two points:

Find the slope of the line:

Find the y-intercept, by substituting coordinates of one point:

The equation becomes:

Find the value of y when x = 22:

Answer:

Step-by-step explanation:

Write it out

[tex](B+6)/4[/tex]

plug in the value

[tex](1.5+6)/4[/tex]

solve

[tex](1.5+6)/4\\7.5/4\\= 1.875[/tex]

The most effectively provide the desired primary data is experimentation

Experimentation is the step in the scientific method that helps people decide between two or more competing explanations—or hypotheses. These hypotheses suggest reasons to explain a phenomenon or predict the results of an action.

With an experiment, you run a test and see what the results are. If you don't get good results, you can try another option, and run another test. Then you can see what the outcomes of the choices are (the info you didn't have when first thinking about the decision), and you can make a better-informed decision now.

According to the question,

A research department wants to test the hypothesis that caffeine from organic coffee more safely stimulates mental alertness than caffeine from nonorganic coffee. Experimentation, one form of primary research, can produce data suggesting cause and effect

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Answer:

a.) The population is years measured after 2000 so 2000 is 0. Any number to the 0 power is 1 so the population is 18.5 (million).

b.) after 8.4 years, so 2008

Step-by-step explanation:

b.) 26.6 = [tex]18.5e^{0.1708t}[/tex]

1.43783784 ≈ [tex]e^{0.1708t}[/tex]

ln 1.43783784= 0.1708t

t=8.4... years

Answer:

x = 10

Step-by-step explanation:

Given equation,

→ -24 - x = -34

Now the value of x will be,

→ -24 - x = -34

→ -x = -34 + 24

→ -x = -10

→ [ x = 10 ]

Hence, the value of x is 10.

Answer: x=10

1. Rearrange the terms

-24 - x= -34

-x - 24= -34

2. Add 24 to both sides

-x - 24= -34

-x - 24= -34

+24 +24

3. Simplify(add the numbers)

-x=-10

4. Divide both sides by the same factor

-x=-10

-x/-1 = -10/-1

Simplify (cancel terms, divide numbers)

X=10

Step-by-step explanation:

A small group communication occurs when three or more people work together interdependently for the purpose of accomplishing a task.

Small Group Communication

Small group communication is the term used to describe face-to-face conversation between more than two people. This kind of internal communication exists.

A small group is typically thought of as a collection of three or less people, with a maximum number of twelve to fifteen. A group would not be considered tiny if it had more than fifteen members or if it had just two.

Since almost all businesses and organisations employ people in small squads, there are advantages or even strengths to small group communication. When compared to one individual working alone on a project, it has been found to be more appropriate and produce better results.

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[tex]\textit{internal division of a line segment using ratios} \\\\\\ A(-8,8)\qquad B(-2,-10)\qquad \qquad \stackrel{\textit{ratio from A to B}}{1:2} \\\\\\ \cfrac{A\underline{C}}{\underline{C} B} = \cfrac{1}{2}\implies \cfrac{A}{B} = \cfrac{1}{2}\implies 2A=1B\implies 2(-8,8)=1(-2,-10)[/tex]

[tex](\stackrel{x}{-16}~~,~~ \stackrel{y}{16})=(\stackrel{x}{-2}~~,~~ \stackrel{y}{-10}) \implies C=\underset{\textit{sum of the ratios}}{\left( \cfrac{\stackrel{\textit{sum of x's}}{-16 -2}}{1+2}~~,~~\cfrac{\stackrel{\textit{sum of y's}}{16 -10}}{1+2} \right)} \\\\\\ C=\left( \cfrac{ -18 }{ 3 }~~,~~\cfrac{ 6}{ 3 } \right)\implies {\Large \begin{array}{llll} C=(-6~~,~~2) \end{array}}[/tex]